DNS for Two-Dimensional Homogeneous Isotropic Turbulence with Initial Large-Scale Vortexes

2017 ◽  
Vol 2017.66 (0) ◽  
pp. 435
Author(s):  
Yusuke OKAMURA ◽  
Masayoshi OKAMOTO
Keyword(s):  
Large Scale ◽  
Isotropic Turbulence ◽  
Two Dimensional ◽  
Homogeneous Isotropic Turbulence

scholarly journals Direct Numerical Simulation in Two Dimensional Homogeneous Isotropic Turbulence Using Spectral Method

2013 ◽  
Vol 5 (3) ◽  
pp. 435-445
Author(s):  
M. S. I. Mallik ◽  
M. A. Uddin ◽  
M. A. Rahman
Keyword(s):  
Numerical Simulation ◽  
Reynolds Number ◽  
Flow Field ◽  
Direct Numerical Simulation ◽  
Spectral Method ◽  
Isotropic Turbulence ◽  
Qualitative Behavior ◽  
Two Dimensional ◽  
Homogeneous Isotropic Turbulence ◽  
Decaying Turbulence

Direct numerical simulation (DNS) in two-dimensional homogeneous isotropic turbulence is performed by using the Spectral method at a Reynolds number Re = 1000 on a uniformly distributed grid points. The Reynolds number is low enough that the computational grid is capable of resolving all the possible turbulent scales. The statistical properties in the computed flow field show a good agreement with the qualitative behavior of decaying turbulence. The behavior of the flow structures in the computed flow field also follow the classical idea of the fluid flow in turbulence. Keywords: Direct numerical simulation, Isotropic turbulence, Spectral method. © 2013 JSR Publications. ISSN: 2070-0237 (Print); 2070-0245 (Online). All rights reserved. doi:http://dx.doi.org/10.3329/jsr.v5i3.12665 J. Sci. Res. 5 (3), 435-445 (2013)  

scholarly journals WKB theory for rapid distortion of inhomogeneous turbulence

1999 ◽  
Vol 390 ◽  
pp. 325-348 ◽  
Author(s):  
S. NAZARENKO ◽  
N. K.-R. KEVLAHAN ◽  
B. DUBRULLE
Keyword(s):  
Large Scale ◽  
Isotropic Turbulence ◽  
Two Dimensional ◽  
Turbulent Spot ◽  
Mean Flow ◽  
Mean Velocity ◽  
Inhomogeneous Turbulence ◽  
Large Scale Vortex ◽  
The Mean ◽  
Mean Strain

A WKB method is used to extend RDT (rapid distortion theory) to initially inhomogeneous turbulence and unsteady mean flows. The WKB equations describe turbulence wavepackets which are transported by the mean velocity and have wavenumbers which evolve due to the mean strain. The turbulence also modifies the mean flow and generates large-scale vorticity via the averaged Reynolds stress tensor. The theory is applied to Taylor's four-roller flow in order to explain the experimentally observed reduction in the mean strain. The strain reduction occurs due to the formation of a large-scale vortex quadrupole structure from the turbulent spot confined by the four rollers. Both turbulence inhomogeneity and three-dimensionality are shown to be important for this effect. If the initially isotropic turbulence is either homogeneous in space or two-dimensional, it has no effect on the large-scale strain. Furthermore, the turbulent kinetic energy is conserved in the two-dimensional case, which has important consequences for the theory of two-dimensional turbulence. The analytical and numerical results presented here are in good qualitative agreement with experiment.

Turbulence in a box: quantification of large-scale resolution effects in isotropic turbulence free decay

2017 ◽  
Vol 818 ◽  
pp. 697-715 ◽  
Author(s):  
M. Meldi ◽  
P. Sagaut
Keyword(s):  
Large Scale ◽  
Isotropic Turbulence ◽  
The Other ◽  
Grid Turbulence ◽  
Physical Domain ◽  
Simulation Studies ◽  
Homogeneous Isotropic Turbulence ◽  
Free Decay ◽  
Reynolds Number Effects ◽  
New Guidelines

The effects of the finiteness of the physical domain over the free decay of homogeneous isotropic turbulence are explored in the present article. Saturation at the large scales is investigated by the use of theoretical analysis and eddy-damped quasi-normal Markovian calculations. Both analyses indicate a strong sensitivity of the large-scale features of the flow to saturation and finite Reynolds number effects. This aspect plays an important role in the general lack of agreement between grid turbulence experiments and numerical simulations. On the other hand, the statistical quantities associated with the behaviour of the spectrum in the inertial region are only marginally affected by saturation. These results suggest new guidelines for the interpretation of experimental and direct numerical simulation studies.

Collision statistics of inertial particles in two-dimensional homogeneous isotropic turbulence with an inverse cascade

2014 ◽  
Vol 745 ◽  
pp. 279-299 ◽  
Author(s):  
Ryo Onishi ◽  
J. C. Vassilicos
Keyword(s):  
Reynolds Number ◽  
Isotropic Turbulence ◽  
Particle System ◽  
Stochastic Simulations ◽  
Collision Kernel ◽  
Inertial Particles ◽  
Two Dimensional ◽  
Homogeneous Isotropic Turbulence ◽  
Local Flow ◽  
Reynolds Number Dependence

AbstractThis study investigates the collision statistics of inertial particles in inverse-cascading two-dimensional (2D) homogeneous isotropic turbulence by means of a direct numerical simulation (DNS). A collision kernel model for particles with small Stokes number ($\mathit{St}$) in 2D flows is proposed based on the model of Saffman & Turner (J. Fluid Mech., vol. 1, 1956, pp. 16–30) (ST56 model). The DNS results agree with this 2D version of the ST56 model for $\mathit{St}\lesssim 0.1$. It is then confirmed that our DNS results satisfy the 2D version of the spherical formulation of the collision kernel. The fact that the flatness factor stays around 3 in our 2D flow confirms that the present 2D turbulent flow is nearly intermittency-free. Collision statistics for $\mathit{St}= 0.1$, 0.4 and 0.6, i.e. for $\mathit{St}<1$, are obtained from the present 2D DNS and compared with those obtained from the three-dimensional (3D) DNS of Onishi et al. (J. Comput. Phys., vol. 242, 2013, pp. 809–827). We have observed that the 3D radial distribution function at contact ($g(R)$, the so-called clustering effect) decreases for $\mathit{St}= 0.4$ and 0.6 with increasing Reynolds number, while the 2D $g(R)$ does not show a significant dependence on Reynolds number. This observation supports the view that the Reynolds-number dependence of $g(R)$ observed in three dimensions is due to internal intermittency of the 3D turbulence. We have further investigated the local $\mathit{St}$, which is a function of the local flow strain rates, and proposed a plausible mechanism that can explain the Reynolds-number dependence of $g(R)$. Meanwhile, 2D stochastic simulations based on the Smoluchowski equations for $\mathit{St}\ll 1$ show that the collision growth can be predicted by the 2D ST56 model and that rare but strong events do not play a significant role in such a small-$\mathit{St}$ particle system. However, the probability density function of local $\mathit{St}$ at the sites of colliding particle pairs supports the view that powerful rare events can be important for particle growth even in the absence of internal intermittency when $\mathit{St}$ is not much smaller than unity.

Kármán–Howarth solutions of homogeneous isotropic turbulence

2021 ◽  
Vol 932 ◽  
Author(s):  
L. Djenidi ◽  
R.A. Antonia
Keyword(s):  
Reynolds Number ◽  
Large Scale ◽  
Isotropic Turbulence ◽  
Three Dimensional ◽  
Order Moment ◽  
Homogeneous Isotropic Turbulence ◽  
The Difference ◽  
Decaying Turbulence ◽  
The Impact ◽  
Good Agreement

The Kármán–Howarth equation (KHEq) is solved using a closure model to obtain solutions of the second-order moment of the velocity increment, $S_2$ , in homogeneous isotropic turbulence (HIT). The results are in good agreement with experimental data for decaying turbulence and are also consistent with calculations based on the three-dimensional energy spectrum for decaying HIT. They differ, however, from those for forced HIT, the difference occurring mainly at large scales. This difference is attributed to the fact that the forcing generates large-scale motions which are not compatible with the KHEq. As the Reynolds number increases, the impact of forcing on the small scales decreases, thus allowing the KHEq and spectrally based solutions to agree well in the range of scales unaffected by forcing. Finally, the results show that the two-thirds law is compatible with the KHEq solutions as the Reynolds number increases to very large, if not infinite, values.

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